The deepest place in the Ocean is the Challenger Deep with a…

The deepest place in the Ocean is the Challenger Deep with a depth of 10,920 m. Suppose you had a balloon filled with air at atmospheric pressure on the surface of the Earth which you took to the bottom of the Challenger Deep. What would the density of the air in the balloon be at the bottom of the Deep? If you dropped the balloon at the bottom, would it rise or fall?  The density of seawater is 1029 kg/cubic meter. Seawater is basically incompressible and a sample of seawater does not change its volume no matter how much pressure it is under. The density of air at 20 C and 1 atm is 1.293*10 -3 kg/m^3. You can assume the temperature at the bottom of the Deep is the same as the temperature at the top. Please answer in kg/m^3

Suppose you fill up your tires with air in the summer when t…

Suppose you fill up your tires with air in the summer when the ambient temperature is 80°F. You fill them up to 35 psi or 241,000 Pa gauge pressure. If the volume of the tire stays the same, and no air enters or leaves the tire, what will the gauge pressure be in winter when the ambient temperature is 15°F?